Mathematical Optimisation with Python

Hereby the curriculum per day:

• Day 1: Review of linear and mixed-integer linear optimisation

  Topics covered:

  • Review of linear optimisation and duality
  • Integer variables and related modelling tricks
  • Introduction to Pyomo modelling language and solvers

  Case study: Recharging strategy for electric vehicle 

  Assignment: Facility location problem

• Day 2: Network optimisation: models and heuristics

  Topics covered:

  • Matching problems
  • Flow and transportation problems
  • Totally unimodularity and its computational advantages

  Case study: Arbitrage search in cryptocurrency markets 

  Assignment: Energy dispatch network problem

• Day 3: Accounting for uncertainty: “Optimisation meets reality”

  Topics covered:

  • Sources of uncertainty
  • Two mindsets to deal with uncertainty
  • The role of simulation and the flaw of averages

  Case study: Fleet assignment 

  Assignment: Multi-day tour plan accounting for availability

• Day 4: Robust optimisation 1 “Optimising for the worst case”

  Topics covered:

  • Core ideas of robust optimisation: worst-case scenarios
  • Types of uncertainty sets and how to build them from data

  Case study: Production plan accounting for uncertainty 

  Assignment: Land allocation with uncertain yield

• Day 5: Robust optimisation 2 “Reformulation and implementation”

  Topics covered:

  • Review of duality and its role in the adversarial approach
  • Robust counterparts: derivation and implementation

  Case study: City routing accounting for traffic disruptions 

  Assignment: Capacitated network inventory-distribution

• Day 6: Stochastic optimisation 1 “Optimising for the average case”

  Topics covered:

  • Probability theory refresher
  • Optimising “on average”: what does it mean?
  • The price of ignoring uncertainty: the flaw of averages

  Case study: Newsvendor problem and its dependency on the demand distribution 

  Assignment: Wind turbine placement problem with wind uncertainty

• Day 7: Stochastic optimisation 2 “Chance constraints and risk measures”

  Topics covered:

  • Modelling using chance constraints
  • MILO reformulation of chance constraints
  • Beyond expectations: an overview of risk measures

  Case study: Investment portfolio optimisation 

  Assignment: Airline seat allocation with stochastic demand

• Day 8: Stochastic optimisation 3 “Advanced stochastic problems and solution methods”

  Topics covered:

  • Two-stage stochastic problem formulation
  • Recourse actions
  • Sample-average approximation

  Case study: Two-stage land allocation problem with uncertain yield 

  Assignment: Energy dispatch and management in the presence of renewables